The commissioner of the Metropolitan Police has apologised to former Cabinet minister Andrew Mitchell after a serving police officer admitted lying about witnessing the row which led to his resignation from Government.

Mr Mitchell welcomed the guilty plea by Pc Keith Wallis to a charge of misconduct in public office, saying that "justice has been done" in the case.

The guilty plea at the Old Bailey led to calls for the former international development secretary and chief whip's return to the Government, which he quit in 2012 after allegations that he had sworn at police and called an officer a "pleb" when he was prevented from cycling out of the gates of Downing Street.

Prime Minister David Cameron welcomed Wallis's guilty plea, saying that it was "completely unacceptable" for police to falsify their account of an incident. But there was no mention in his brief statement issued by Number Ten of whether the development will open the door for a return to ministerial office for Mr Mitchell.

Wallis, 53, of West Drayton, west London, was charged after sending an email to Conservative deputy chief whip John Randall, who was his MP, wrongly claiming that he had seen what happened as Mr Mitchell left Downing Street on September 19, 2012.

The then chief whip became involved in a heated confrontation with another police officer, Toby Rowland, after he was refused permission to cycle through the main gate. The Sutton Coldfield MP later admitted swearing but denied Pc Rowland's claim that he used the word ''pleb''.

"I am pleased that justice has been done in a criminal court today," he said in a statement.

"It is very sad and worrying for all of us that a serving police officer should have behaved in this way. There remain many questions unanswered; in particular why Pc Wallis wrote this email and who else was involved in this process.

"I am looking forward to seeing justice done in the up to 10 other related disciplinary cases involving police officers so that I can focus all my energy on delivering for my constituents and help David Cameron win a Conservative majority at the 2015 election."

Mr Cameron said: "It is completely unacceptable for a serving police officer to falsify an account of any incident. Andrew Mitchell has consistently denied the version of events presented in the email and I welcome the fact that the officer concerned has now pleaded guilty."

He said: "This investigation has been a ruthless search for the truth as at the heart of this are extremely damaging allegations that officers have lied and falsified statements against a Cabinet minister.

"The evidence against Pc Wallis was such that he has entered a guilty plea. To lie about witnessing something and provide a false account falls way below the standards that I and Pc Wallis's colleagues expect of police officers. His actions have also negatively impacted upon public trust and confidence in the integrity of police officers.

"I would also like to apologise to Mr Mitchell that an MPS (Metropolitan Police Service) officer clearly lied about seeing him behaving in a certain manner. I will be writing to him offering to meet and apologise in person."

Wallis, wearing a black suit and tie, stood in the dock and spoke only to confirm his name and that he understood the charge before entering his guilty plea.

The court heard that Wallis, who is from the Metropolitan Police diplomatic protection group, admitted the offence in police interview and offered to resign.

He released Wallis on unconditional bail but warned him that "all sentencing options remain open to the court".

Following reports of the Plebgate incident, Mr Mitchell apologised for being disrespectful to police but denied using the words attributed to him.

But his apology was not enough to prevent members of the Police Federation of England and Wales protesting at the Conservative Party's annual conference in T-shirts bearing the slogan "Pc Pleb and Proud".

After meeting the MP in Sutton Coldfield, the Federation's Inspector Ken MacKaill said he had "no option but to resign", while Labour leader Ed Miliband described him as "toast" in the House of Commons and Mr Cameron himself said his chief whip was wrong to use the words he did.

The unrelenting pressure eventually led Mr Mitchell to offer his resignation on October 19, a month after the initial altercation.

Today, the Federation's chairman, Steve Williams, said: "Despite the high-profile nature of the case and the officer's regrettable actions, one officer admitting one offence should not be allowed to undermine public confidence in the police service.

"There are nearly 130,000 police officers in England and Wales, the vast majority of whom conduct themselves with the utmost integrity and professionalism at all times, often risking their own safety in the interests of the general public and the communities they serve."

Conservative MP Sir Richard Ottaway suggested Sir Bernard may end up having to quit over the row.

Sir Richard told BBC Radio 4's World At One programme: "It's a very black day for the Met... Don't forget that Mr Hogan-Howe said right at the outset that he had 100% confidence in his officers and I think he would be the first to admit now perhaps that was a bit of a misjudgment."

Asked if he ruled out the possibility of the police chief having to quit, he replied: "Obviously people will call for his resignation. I personally don't want to make a judgment on that at the moment.

"As a London Member of Parliament, I actually think he is a pretty good Metropolitan Commissioner but if there is, at the end of this, you know, we find ourselves facing the situation whereby he has made a serious misjudgment on this then, no doubt, he will be thinking very hard about his future."

Prominent Labour MP Tom Watson called for Mr Mitchell to be restored to the Cabinet.

He told World At One: "It's been pretty clear to me for some time that Andrew Mitchell has had a great injustice done to him.

"The decision of the police officer to resign and plead guilty today is further vindication that he's paid a terrible price."

He added: "In situations like this, when these spats get out of control and end up being media frenzies, then the best way to do it is to put the matter right and move on and I think the outcome that will achieve that is for him to get a job back in the Cabinet as quickly as possible so that he can conduct public office at the highest level as he was before."

Conservative Michael Ellis, who sits on the Commons Home Affairs Select Committee, said it was a "major crisis for the Metropolitan Police".

The committee's chairman, Keith Vaz, said: "This plea is not only the first public acknowledgement that Mr Mitchell has been the subject of gross unfairness but it also an admission that a criminal offence has been committed against him.

"With 11 other officers being subject to misconduct hearings, and the further investigation by the IPCC, this appears to be a complete vindication of Mr Mitchell's position."

Mr Vaz said Sir Bernard was right to apologise, adding: "Taken with the apologies of the other Chief Constables, it shows that the internal mechanisms of the police have not worked on this occasion. Lessons have to be learnt in order to restore full public confidence in way these matters are dealt with.

"Now is the time to turn the page on this whole unfortunate incident, which took only 45 seconds but has cost the taxpayer hundreds of thousands of pounds, Mr Mitchell his job and damaged the reputation of the police."

Shadow home secretary Yvette Cooper said Wallis's actions "risk casting a shadow over the excellent work police officers do day in, day out".

Ms Cooper said: "Democracy depends on the idea that everyone can rely on the police to treat them with honesty and fairness, without fear or favour - from Cabinet ministers to teenagers in the street or victims of crime. So it is of great concern when those we trust fall below the standards the police and the public expect."

Last month the Police Federation confirmed that the officer at the centre of the row was to sue Mr Mitchell.

Pc Rowland issued a letter of claim for libel against Mr Mitchell relating to the issue in the wake of their differing accounts of the heated confrontation in Downing Street.

Prosecutors have found there was insufficient evidence to charge Pc Rowland with any criminal offence after the row, and Scotland Yard has said he will not face disciplinary action.

Mr Mitchell previously said he hoped the officer would give evidence on oath as part of the libel proceedings against the Sun newspaper. But Mr Rowland said he stood by his account of what was said.